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Unconditional ideals in Banach spaces

G. GodefroyN. KaltonP. Saphar — 1993

Studia Mathematica

We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition X * * * = X X * is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel X . We undertake a general study of h-ideals and u-ideals. For example we show that...

Unsolved Problems

1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

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